The 33-year-old will initially join the Blades until the end of the campaign, at which point there is a clause to extend his contract by a further 12 months.
Donaldson has spent time at nine different clubs during his senior career, most recently scoring 33 times in 102 league starts for Birmingham upon joining from Brentford in 2014.
United boss Chris Wilder told United's official website: "We have watched Clayton a lot, most recently for Birmingham at Burton, and it is clear that he will be a useful addition for us.
"He offers additional pace and power at the top end of the pitch and his Championship experience will be of value."
United also completed the signing of Motherwell defender Ben Heneghan on deadline day, taking their number of new arrivals this summer to 10 in all.